The 25-year-old Connolly, a native of Bloomington, MN, has five goals and 31 assists in 44 games this season, which ranks him second in scoring with the Rockford Icehogs of the American Hockey League. He originally signed with the Blackhawks on June 8, 2009.
"As we projected our line-up going forward we felt it was going to be difficult for us to find a spot for Brendan or get him significant ice-time," general manager Jay Feaster said in a statement. "Given his pending UFA status and the fact that we were not going to re-sign him, we felt it important to try to move him for another asset. In Brian Connelly we obtain a 25-year-old highly skilled AHL All-Star defenseman who is still a legitimate prospect. We are excited to have Brian in the organization."
Morrison, 36, has appeared in 923 career NHL regular season games over parts of 15 seasons, collecting 200 goals and 446 penalty minutes. The Pitt Meadows, British Columbia, native, has spent last two years with the Flames. He has seven assists and 11 points in 28 games this season.
Morrison has reached the Stanley Cup Playoffs nine times during his career, racking up eight goals and 21 assists and 40 penalty minutes in 58 post-seasons. He has skated for the New Jersey Devils, Vancouver Canucks, Anaheim Ducks, Dallas Stars, Washington Capitals and Flames.